Rogowski coils

1. The problem statement, all variables and given/known data
When a wire carries an AC current with a known frequency you can use a Rogowski
coil to determine the amplitude Imax of the current without disconnecting the wire to
shunt the current in a meter. The Rogowski coil, shown in the ﬁgure, simply clips
around the wire. It consists of a toroidal conductor wrapped around a circular return
cord. The toroid has n turns per unit length and a cross-sectional area A. The current
to be measured is given by I(t) = Imax sin (ω t). (a) Show that the amplitude, E, of the
emf induced in the Rogowski coil is E = μ0 n A ω Imax. (b) Explain why the wire
carrying the unknown current need not be at the center of the Rogowski coil, and why
the coil will not respond to nearby currents that it does not enclose.

2. Relevant equations

Emf= -N(dI/dt) where I = magnetic flux, not current

Emf = I/R = R*(dQ/dt) where I = current

Magnetic flux = *integral* (B*dA)

Emf = *surface integral* (E*dL) = -(d*magnetic flux*/dt)

Emf= (ANu/l)*(dI/dt)

3. The attempt at a solution
I am not really sure where to start - maybe by using the Emf= (ANu/l)*(dI/dt) ?? Can anyone help get me started in the right direction? Thanks!

**In the attached document, the diagram is in #6, all the way at the bottom**

Edit: The figure is simply a ring of wire that has another wire wrapped around it, with a current going through the ring. Apologies for the mix up